Legendary Pokemon aren't a species, and often they are genderless. They're a throwback to various gods. As such, there is supposed to be only one of each. They can't breed.
– Gorchestopher HJul 13 '16 at 15:47

@JoãoVictorOliveira Correct, but until Gen 5, both groups were referred to as "legendary Pokémon" outside of Japan. Many people still aren't aware of the distinction, and some still call them all "legendaries" out of habit.
– Mike KelloggJul 15 '16 at 22:25

5 Answers
5

There are multiples of at least some Legendary Pokémon in the anime

While it can't be said for certain for every Legendary, a number of them are explicitly shown to have multiple members of the species and/or be capable of breeding.

Lugia - A parent and child pair appear together in the Johto League series of the anime.

Latios and Latias - These two make multiple appearances, including Latios dying during movie 5, then other Latios appearing later in the series, while a Latias in the possession of a Nurse Joy can be seen at one point in the series, only for a wild one to appear later.

Genesect1 - Five Genesect (one of which is Shiny) all appear together at one point during the anime, and later in the 16th movie. (Thanks to @Axelrod)

Add Mewtwo, who is a different specimen between The First Movie and the Genesect movie, and Genesect who is one of many Genesect in the Genesect movie. Genesect Genesect Genesect Genesect.
– Slacklord the TerribleJul 14 '16 at 21:34

@Axelrod I'd heard about the different Mewtwos before, but I can't find anything on Bulbapedia that seems conclusive enough to show they're different. I haven't watched movie 16 before, is it obvious that Mewtwo doesn't recognize Ash?
– Mike KelloggJul 14 '16 at 21:47

@Axelrod Nevermind, I found signs that the creation process went a bit differently. Thanks.
– Mike KelloggJul 14 '16 at 21:52

2

No problem. Also, the Mewtwo in the new movie is female-voiced, while the First movie Mewtwo was male-voiced.
– Slacklord the TerribleJul 14 '16 at 21:56

Rayquaza- There was a shiny Rayquaza in the Hoopa movie, yet there was a normal rayquaza in the deoxys movie.

Also...Diancie- although mythical and not legendary, it's still rare. Yet, Diancie is formed by a mutation in Carbink, meaning there can essentially be more than one Princess Diancie.

Solgaleo/Lunala- Are legendary on our world, yet there are wild cosmog in the alternate dimension where they come from.

Legendary Dog Trio- Shiny versions of them can be seen in the zoroark movie, yet in pokemon chronicles Gold/Ethan encounters a normal Raikou(If I can remember correctly), and Ash has seen a normal colored Suicune and Entei in their respective movies.

Zekrom/Reshiram- This is my personal theory....in the Hoopa movie Zekrom and Reshiram can be seen well and alive, yet Kyurem could still become Black/White Kyurem even though it needs to absorb the two in stone form......soooo maybe there are multiple Zekrom and Reshiram?

My answer is: yes. I do believe there are multiple legendary Pokemon. However, to an extent. If anything, maybe all the legendary Pokemon have more than one each, even Kyogre and Groudon. However I think it stops with the creation trio as well as with Arceus, they may be the only ones of their kind. But as for the rest, definitely more than one each. Just my theory though.

Yes there are multiple pokemon of certain legendaries and mythicals. We know this because of Deoxys, there are multiple Deoxys in both the manga and movie about them showcasing that there are 2 known Deoxys. This can also be applied to Manaphy and that you can create multiple Phione from Manaphy, Cosmog is also included in this since there are clearly more then one cosmog.

Aside from the high statistics shared by most Legendary Pokémon, many can only be obtained once per save file (excluding Pokémon events); in order to obtain multiple, a player would need to trade for one.

You can understand a "save file" as the universe. The anime can be a "save file" where the player is the main character (Ash, for example). And considering the anime is based in the game, if there's only one specimen of each legendary Pokémon for each save file, then it is safe to assume there's only one specimen of each legendary Pokémon in the anime.

"per save file" indicates the game mechanic. I am looking for answers outside of that. Sorry if that was not clear.
– SkoobaJul 13 '16 at 19:24

1

@Skooba I understood that, but if you think about it, you can understand a "save file" as the universe. The anime can be a "save file" where the player is the main character (Ash, for example). And considering the anime is based in the game, if there's only 1 specimen of each legendary Pokémon for each save file, then it is safe to assume there's only 1 specimen of each legendary Pokémon in the anime.
– João Victor OliveiraJul 14 '16 at 17:00

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